Set of orbital elements of a celestial body naturally originating from dynamic problem solution is proposed. Orbital elements considered are 4 spherical coordinates of radius-vector and body velocity vector for the moment of passing a pericenter and time of this passing. Dependencies, connecting proposed orbital elements and conventional orbital elements of celestial mechanics have been determined. These enable one to perform direct and inverse coordinate transformations. Advantages of usage of natural orbital elements have been illustrated by example in which probability distributions of natural orbital elements for comets have been determined. Analysis of these probabilities enables one to make some suggestions on comets origin and to classify them accordingly. Another advantage of usage of natural orbital elements consists in determination of analytical dependence between a perihelion velocity and a perihelion distance.